Holomorphic disks and knot invariants

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Abstract

We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, and a description of the behavior under connected sums. Then, we establish a relationship with HF+ for surgeries along the knot. Applications include calculation of HF+ of three-manifolds obtained by surgeries on some special knots in S3, and also calculation of HF+ for certain simple three-manifolds which fiber over the circle.

Original languageEnglish (US)
Pages (from-to)58-116
Number of pages59
JournalAdvances in Mathematics
Volume186
Issue number1
DOIs
StatePublished - Aug 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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